User registration can happen either on your site or as the user actually completes a checkout. The first step is to determine which method makes more sense. If there's a reason for a user to register prior to allowing a checkout, you can use the API and single sign-on. Create the user via the API when the user is created on your end, then use SSO to force a valid session prior to allowing through to checkout.

The alternate method would be to allow the users to register using the FoxyCart checkout. You'd then process the XML datafeed to create the user immediately upon successful transaction.

You could use both approaches, but you'll want to make it clear via links and instructions to your users exactly what's going on.

Regardless the method of user registration you choose (above), the basic idea is covered here.